Shear layer solutions of incompressible MHD and dynamo effect

David Gérard-Varet; Frédéric Rousset

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 5, page 677-710
  • ISSN: 0294-1449

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Gérard-Varet, David, and Rousset, Frédéric. "Shear layer solutions of incompressible MHD and dynamo effect." Annales de l'I.H.P. Analyse non linéaire 24.5 (2007): 677-710. <http://eudml.org/doc/78755>.

@article{Gérard2007,
author = {Gérard-Varet, David, Rousset, Frédéric},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {WKB expansions; nonlinear instability; stretch-diffuse mechanism},
language = {eng},
number = {5},
pages = {677-710},
publisher = {Elsevier},
title = {Shear layer solutions of incompressible MHD and dynamo effect},
url = {http://eudml.org/doc/78755},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Gérard-Varet, David
AU - Rousset, Frédéric
TI - Shear layer solutions of incompressible MHD and dynamo effect
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 5
SP - 677
EP - 710
LA - eng
KW - WKB expansions; nonlinear instability; stretch-diffuse mechanism
UR - http://eudml.org/doc/78755
ER -

References

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  1. [1] Chossat P., Iooss G., The Couette–Taylor Problem, Applied Mathematical Sciences, vol. 102, Springer-Verlag, New York, 1994. Zbl0817.76001
  2. [2] Desjardins B., Grenier E., Linear instability implies nonlinear instability for various types of viscous boundary layers, Ann. Inst. H. Poincaré Anal. Non Linéaire20 (1) (2003) 87-106. Zbl1114.76024MR1958163
  3. [3] Fearn D., Hydromagnetic flows in planetary cores, Rep. Prog. Phys.61 (1998) 175-235. 
  4. [4] Gailitis A., Lielausis O., Platacis E., Gerbeth G., Stefani F., Riga dynamo experiment and its theoretical background, Phys. Plasmas11 (5) (2004) 2838-2843. MR2062703
  5. [5] Gérard-Varet D., Oscillating solutions of incompressible MHD and dynamo effect, SIAM J. Math. Anal.37 (3) (2005) 815-840. Zbl1141.76479MR2191778
  6. [6] Gilbert A.D., Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dynamics44 (1988) 241-258. Zbl0676.76096
  7. [7] Gilbert A.D., Dynamo theory, in: Handbook of Mathematical Fluid Dynamics, vol. II, North-Holland, Amsterdam, 2003, pp. 355-441. Zbl1033.76061MR1984156
  8. [8] Goodman J., Xin Z.P., Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rational Mech. Anal.121 (3) (1992) 235-265. Zbl0792.35115MR1188982
  9. [9] Grenier E., On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math.53 (9) (2000) 1067-1091. Zbl1048.35081MR1761409
  10. [10] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. Zbl0456.35001MR610244
  11. [11] Ponomarenko Y., On the theory of hydromagnetic dynamos, Zh. Prikl. Mekh. Tekh. Fiz. (USSR)44 (1973) 47-51. 
  12. [12] Roberts P., An Introduction to Magnetohydrodynamics, Longmans, Green, 1967. 

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